%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KRS088+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:01:06 EDT 2022
% Result : Unsatisfiable 1.31s 1.72s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 9 unt; 0 nHn; 16 RR)
% Number of literals : 26 ( 2 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(17,axiom,
( ~ cUnsatisfiable(A)
| rf(A,dollar_f2(A)) ),
file('KRS088+1.p',unknown),
[] ).
cnf(18,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvF(dollar_f2(A),B)
| rf(B,dollar_f1(A,B)) ),
file('KRS088+1.p',unknown),
[] ).
cnf(19,axiom,
( ~ cUnsatisfiable(A)
| ~ rinvF(dollar_f2(A),B)
| ~ cp1(dollar_f1(A,B)) ),
file('KRS088+1.p',unknown),
[] ).
cnf(20,axiom,
( ~ cUnsatisfiable(A)
| cp1(dollar_f2(A)) ),
file('KRS088+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ rf(A,B)
| ~ rf(A,C)
| B = C ),
file('KRS088+1.p',unknown),
[] ).
cnf(25,axiom,
( rinvF(A,B)
| ~ rf(B,A) ),
file('KRS088+1.p',unknown),
[] ).
cnf(33,axiom,
cUnsatisfiable(i2003_11_14_17_19_49673),
file('KRS088+1.p',unknown),
[] ).
cnf(34,plain,
cp1(dollar_f2(i2003_11_14_17_19_49673)),
inference(hyper,[status(thm)],[33,20]),
[iquote('hyper,33,20')] ).
cnf(35,plain,
rf(i2003_11_14_17_19_49673,dollar_f2(i2003_11_14_17_19_49673)),
inference(hyper,[status(thm)],[33,17]),
[iquote('hyper,33,17')] ).
cnf(39,plain,
rinvF(dollar_f2(i2003_11_14_17_19_49673),i2003_11_14_17_19_49673),
inference(hyper,[status(thm)],[35,25]),
[iquote('hyper,35,25')] ).
cnf(43,plain,
rf(i2003_11_14_17_19_49673,dollar_f1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673)),
inference(hyper,[status(thm)],[39,18,33]),
[iquote('hyper,39,18,33')] ).
cnf(47,plain,
rinvF(dollar_f1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673),i2003_11_14_17_19_49673),
inference(hyper,[status(thm)],[43,25]),
[iquote('hyper,43,25')] ).
cnf(49,plain,
dollar_f2(i2003_11_14_17_19_49673) = dollar_f1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673),
inference(hyper,[status(thm)],[43,23,35]),
[iquote('hyper,43,23,35')] ).
cnf(55,plain,
cp1(dollar_f1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[34]),49]),
[iquote('back_demod,34,demod,49')] ).
cnf(64,plain,
( ~ rinvF(dollar_f1(i2003_11_14_17_19_49673,i2003_11_14_17_19_49673),A)
| ~ cp1(dollar_f1(i2003_11_14_17_19_49673,A)) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[49,19]),33]),
[iquote('para_from,48.1.1,19.2.1,unit_del,33')] ).
cnf(70,plain,
$false,
inference(hyper,[status(thm)],[64,47,55]),
[iquote('hyper,64,47,55')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KRS088+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 03:47:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.31/1.72 ----- Otter 3.3f, August 2004 -----
% 1.31/1.72 The process was started by sandbox on n027.cluster.edu,
% 1.31/1.72 Wed Jul 27 03:47:21 2022
% 1.31/1.72 The command was "./otter". The process ID is 6477.
% 1.31/1.72
% 1.31/1.72 set(prolog_style_variables).
% 1.31/1.72 set(auto).
% 1.31/1.72 dependent: set(auto1).
% 1.31/1.72 dependent: set(process_input).
% 1.31/1.72 dependent: clear(print_kept).
% 1.31/1.72 dependent: clear(print_new_demod).
% 1.31/1.72 dependent: clear(print_back_demod).
% 1.31/1.72 dependent: clear(print_back_sub).
% 1.31/1.72 dependent: set(control_memory).
% 1.31/1.72 dependent: assign(max_mem, 12000).
% 1.31/1.72 dependent: assign(pick_given_ratio, 4).
% 1.31/1.72 dependent: assign(stats_level, 1).
% 1.31/1.72 dependent: assign(max_seconds, 10800).
% 1.31/1.72 clear(print_given).
% 1.31/1.72
% 1.31/1.72 formula_list(usable).
% 1.31/1.72 all A (A=A).
% 1.31/1.72 all A B (A=B&cUnsatisfiable(A)->cUnsatisfiable(B)).
% 1.31/1.72 all A B (A=B&cowlNothing(A)->cowlNothing(B)).
% 1.31/1.72 all A B (A=B&cowlThing(A)->cowlThing(B)).
% 1.31/1.72 all A B (A=B&cp1(A)->cp1(B)).
% 1.31/1.72 all A B C (A=B&rf(A,C)->rf(B,C)).
% 1.31/1.72 all A B C (A=B&rf(C,A)->rf(C,B)).
% 1.31/1.72 all A B C (A=B&rinvF(A,C)->rinvF(B,C)).
% 1.31/1.72 all A B C (A=B&rinvF(C,A)->rinvF(C,B)).
% 1.31/1.72 all A B C (A=B&rinvR(A,C)->rinvR(B,C)).
% 1.31/1.72 all A B C (A=B&rinvR(C,A)->rinvR(C,B)).
% 1.31/1.72 all A B C (A=B&rr(A,C)->rr(B,C)).
% 1.31/1.72 all A B C (A=B&rr(C,A)->rr(C,B)).
% 1.31/1.72 all A B (A=B&xsd_integer(A)->xsd_integer(B)).
% 1.31/1.72 all A B (A=B&xsd_string(A)->xsd_string(B)).
% 1.31/1.72 all X (cowlThing(X)& -cowlNothing(X)).
% 1.31/1.72 all X (xsd_string(X)<-> -xsd_integer(X)).
% 1.31/1.72 all X (cUnsatisfiable(X)<-> (exists Y (rf(X,Y)& (all Z (rinvF(Y,Z)-> (exists W (rf(Z,W)& -cp1(W)))))&cp1(Y)))).
% 1.31/1.72 all X Y Z (rf(X,Y)&rf(X,Z)->Y=Z).
% 1.31/1.72 all X Y (rinvF(X,Y)<->rf(Y,X)).
% 1.31/1.72 all X Y (rinvR(X,Y)<->rr(Y,X)).
% 1.31/1.72 all X Y Z (rr(X,Y)&rr(Y,Z)->rr(X,Z)).
% 1.31/1.72 cUnsatisfiable(i2003_11_14_17_19_49673).
% 1.31/1.72 end_of_list.
% 1.31/1.72
% 1.31/1.72 -------> usable clausifies to:
% 1.31/1.72
% 1.31/1.72 list(usable).
% 1.31/1.72 0 [] A=A.
% 1.31/1.72 0 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.31/1.72 0 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.31/1.72 0 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.31/1.72 0 [] A!=B| -cp1(A)|cp1(B).
% 1.31/1.72 0 [] A!=B| -rf(A,C)|rf(B,C).
% 1.31/1.72 0 [] A!=B| -rf(C,A)|rf(C,B).
% 1.31/1.72 0 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 1.31/1.72 0 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 1.31/1.72 0 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.31/1.72 0 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.31/1.72 0 [] A!=B| -rr(A,C)|rr(B,C).
% 1.31/1.72 0 [] A!=B| -rr(C,A)|rr(C,B).
% 1.31/1.72 0 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.31/1.72 0 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.31/1.72 0 [] cowlThing(X).
% 1.31/1.72 0 [] -cowlNothing(X).
% 1.31/1.72 0 [] -xsd_string(X)| -xsd_integer(X).
% 1.31/1.72 0 [] xsd_string(X)|xsd_integer(X).
% 1.31/1.72 0 [] -cUnsatisfiable(X)|rf(X,$f2(X)).
% 1.31/1.72 0 [] -cUnsatisfiable(X)| -rinvF($f2(X),Z)|rf(Z,$f1(X,Z)).
% 1.31/1.72 0 [] -cUnsatisfiable(X)| -rinvF($f2(X),Z)| -cp1($f1(X,Z)).
% 1.31/1.72 0 [] -cUnsatisfiable(X)|cp1($f2(X)).
% 1.31/1.72 0 [] cUnsatisfiable(X)| -rf(X,Y)|rinvF(Y,$f3(X,Y))| -cp1(Y).
% 1.31/1.72 0 [] cUnsatisfiable(X)| -rf(X,Y)| -rf($f3(X,Y),W)|cp1(W)| -cp1(Y).
% 1.31/1.72 0 [] -rf(X,Y)| -rf(X,Z)|Y=Z.
% 1.31/1.72 0 [] -rinvF(X,Y)|rf(Y,X).
% 1.31/1.72 0 [] rinvF(X,Y)| -rf(Y,X).
% 1.31/1.72 0 [] -rinvR(X,Y)|rr(Y,X).
% 1.31/1.72 0 [] rinvR(X,Y)| -rr(Y,X).
% 1.31/1.72 0 [] -rr(X,Y)| -rr(Y,Z)|rr(X,Z).
% 1.31/1.72 0 [] cUnsatisfiable(i2003_11_14_17_19_49673).
% 1.31/1.72 end_of_list.
% 1.31/1.72
% 1.31/1.72 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.31/1.72
% 1.31/1.72 This ia a non-Horn set with equality. The strategy will be
% 1.31/1.72 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.31/1.72 deletion, with positive clauses in sos and nonpositive
% 1.31/1.72 clauses in usable.
% 1.31/1.72
% 1.31/1.72 dependent: set(knuth_bendix).
% 1.31/1.72 dependent: set(anl_eq).
% 1.31/1.72 dependent: set(para_from).
% 1.31/1.72 dependent: set(para_into).
% 1.31/1.72 dependent: clear(para_from_right).
% 1.31/1.72 dependent: clear(para_into_right).
% 1.31/1.72 dependent: set(para_from_vars).
% 1.31/1.72 dependent: set(eq_units_both_ways).
% 1.31/1.72 dependent: set(dynamic_demod_all).
% 1.31/1.72 dependent: set(dynamic_demod).
% 1.31/1.72 dependent: set(order_eq).
% 1.31/1.72 dependent: set(back_demod).
% 1.31/1.72 dependent: set(lrpo).
% 1.31/1.72 dependent: set(hyper_res).
% 1.31/1.72 dependent: set(unit_deletion).
% 1.31/1.72 dependent: set(factor).
% 1.31/1.72
% 1.31/1.72 ------------> process usable:
% 1.31/1.72 ** KEPT (pick-wt=7): 1 [] A!=B| -cUnsatisfiable(A)|cUnsatisfiable(B).
% 1.31/1.72 ** KEPT (pick-wt=7): 2 [] A!=B| -cowlNothing(A)|cowlNothing(B).
% 1.31/1.72 ** KEPT (pick-wt=7): 3 [] A!=B| -cowlThing(A)|cowlThing(B).
% 1.31/1.72 ** KEPT (pick-wt=7): 4 [] A!=B| -cp1(A)|cp1(B).
% 1.31/1.72 ** KEPT (pick-wt=9): 5 [] A!=B| -rf(A,C)|rf(B,C).
% 1.31/1.72 ** KEPT (pick-wt=9): 6 [] A!=B| -rf(C,A)|rf(C,B).
% 1.31/1.72 ** KEPT (pick-wt=9): 7 [] A!=B| -rinvF(A,C)|rinvF(B,C).
% 1.31/1.72 ** KEPT (pick-wt=9): 8 [] A!=B| -rinvF(C,A)|rinvF(C,B).
% 1.31/1.72 ** KEPT (pick-wt=9): 9 [] A!=B| -rinvR(A,C)|rinvR(B,C).
% 1.31/1.72 ** KEPT (pick-wt=9): 10 [] A!=B| -rinvR(C,A)|rinvR(C,B).
% 1.31/1.72 ** KEPT (pick-wt=9): 11 [] A!=B| -rr(A,C)|rr(B,C).
% 1.31/1.72 ** KEPT (pick-wt=9): 12 [] A!=B| -rr(C,A)|rr(C,B).
% 1.31/1.72 ** KEPT (pick-wt=7): 13 [] A!=B| -xsd_integer(A)|xsd_integer(B).
% 1.31/1.72 ** KEPT (pick-wt=7): 14 [] A!=B| -xsd_string(A)|xsd_string(B).
% 1.31/1.72 ** KEPT (pick-wt=2): 15 [] -cowlNothing(A).
% 1.31/1.72 ** KEPT (pick-wt=4): 16 [] -xsd_string(A)| -xsd_integer(A).
% 1.31/1.72 ** KEPT (pick-wt=6): 17 [] -cUnsatisfiable(A)|rf(A,$f2(A)).
% 1.31/1.72 ** KEPT (pick-wt=11): 18 [] -cUnsatisfiable(A)| -rinvF($f2(A),B)|rf(B,$f1(A,B)).
% 1.31/1.72 ** KEPT (pick-wt=10): 19 [] -cUnsatisfiable(A)| -rinvF($f2(A),B)| -cp1($f1(A,B)).
% 1.31/1.72 ** KEPT (pick-wt=5): 20 [] -cUnsatisfiable(A)|cp1($f2(A)).
% 1.31/1.72 ** KEPT (pick-wt=12): 21 [] cUnsatisfiable(A)| -rf(A,B)|rinvF(B,$f3(A,B))| -cp1(B).
% 1.31/1.72 ** KEPT (pick-wt=14): 22 [] cUnsatisfiable(A)| -rf(A,B)| -rf($f3(A,B),C)|cp1(C)| -cp1(B).
% 1.31/1.72 ** KEPT (pick-wt=9): 23 [] -rf(A,B)| -rf(A,C)|B=C.
% 1.31/1.72 ** KEPT (pick-wt=6): 24 [] -rinvF(A,B)|rf(B,A).
% 1.31/1.72 ** KEPT (pick-wt=6): 25 [] rinvF(A,B)| -rf(B,A).
% 1.31/1.72 ** KEPT (pick-wt=6): 26 [] -rinvR(A,B)|rr(B,A).
% 1.31/1.72 ** KEPT (pick-wt=6): 27 [] rinvR(A,B)| -rr(B,A).
% 1.31/1.72 ** KEPT (pick-wt=9): 28 [] -rr(A,B)| -rr(B,C)|rr(A,C).
% 1.31/1.72 15 back subsumes 2.
% 1.31/1.72
% 1.31/1.72 ------------> process sos:
% 1.31/1.72 ** KEPT (pick-wt=3): 30 [] A=A.
% 1.31/1.72 ** KEPT (pick-wt=2): 31 [] cowlThing(A).
% 1.31/1.72 ** KEPT (pick-wt=4): 32 [] xsd_string(A)|xsd_integer(A).
% 1.31/1.72 ** KEPT (pick-wt=2): 33 [] cUnsatisfiable(i2003_11_14_17_19_49673).
% 1.31/1.72 Following clause subsumed by 30 during input processing: 0 [copy,30,flip.1] A=A.
% 1.31/1.72 30 back subsumes 29.
% 1.31/1.72 31 back subsumes 3.
% 1.31/1.72
% 1.31/1.72 ======= end of input processing =======
% 1.31/1.72
% 1.31/1.72 =========== start of search ===========
% 1.31/1.72
% 1.31/1.72 -------- PROOF --------
% 1.31/1.72
% 1.31/1.72 -----> EMPTY CLAUSE at 0.00 sec ----> 70 [hyper,64,47,55] $F.
% 1.31/1.72
% 1.31/1.72 Length of proof is 8. Level of proof is 5.
% 1.31/1.72
% 1.31/1.72 ---------------- PROOF ----------------
% 1.31/1.72 % SZS status Theorem
% 1.31/1.72 % SZS output start Refutation
% See solution above
% 1.31/1.72 ------------ end of proof -------------
% 1.31/1.72
% 1.31/1.72
% 1.31/1.72 Search stopped by max_proofs option.
% 1.31/1.72
% 1.31/1.72
% 1.31/1.72 Search stopped by max_proofs option.
% 1.31/1.72
% 1.31/1.72 ============ end of search ============
% 1.31/1.72
% 1.31/1.72 -------------- statistics -------------
% 1.31/1.72 clauses given 14
% 1.31/1.72 clauses generated 102
% 1.31/1.72 clauses kept 68
% 1.31/1.72 clauses forward subsumed 73
% 1.31/1.72 clauses back subsumed 3
% 1.31/1.72 Kbytes malloced 976
% 1.31/1.72
% 1.31/1.72 ----------- times (seconds) -----------
% 1.31/1.72 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.31/1.72 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.31/1.72 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.31/1.72
% 1.31/1.72 That finishes the proof of the theorem.
% 1.31/1.72
% 1.31/1.72 Process 6477 finished Wed Jul 27 03:47:23 2022
% 1.31/1.72 Otter interrupted
% 1.31/1.72 PROOF FOUND
%------------------------------------------------------------------------------